Carried items only fit in stockpiles and vehicles (not chests), when you target one it will show you how to put stuff there with just clicks, alternatively you can open their inventories with e and move it manually. You're supposed to shovel your dirt right into a cart and bring it to a stockpile. You can never carry more than 20 on your player. Works the same for any other carried object. We didn't want you to have a infinite minecraft-like inventory, but to use objects you need to build infrastructure for and be limited in what you can carry without machinery to help you. It's a major factor for Eco's economy to work out and simply a different, more realistic approach that fits the goal of Eco as a society simulation.
You're the first person in my five years at SLG that mentioned to have a problem with this concept and I'm unable to find the people asking the same question for the past 5 years at all, so this is surprising to me. Do you maybe not see the interaction hints over stockpiles and carts due to some bug? Did you check out Ecopedia for the basics (F1)? Watched a gameplay video, as basically any video about Eco should show how it works, it's such a basic thing people need to do all the time?